Question

Sachs Brands' defined benefit pension plan specifies annual retirement benefits equal to: 1.2% × service years × final year's salary, payable at the end of each year. Angela Davenport was hired by Sachs at the beginning of 2004 and is expected to retire at the end of 2038 after 35 years' service. Her retirement is expected to span 18 years. Davenport's salary is $80,000 at the end of 2018 and the company's actuary projects her salary to be $230,000 at retirement. The actuary's discount rate is 6%. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)

Required:
2. Estimate by the projected benefits approach the amount of Davenport's annual retirement payments earned as of the end of 2018.
3. What is the company's projected benefit obligation at the end of 2018 with respect to Davenport? (Do not round intermediate calculations. Round your final answer to nearest whole dollar.)
4. If no estimates are changed in the meantime, what will be the company's projected benefit obligation at the end of 2021 (three years later) with respect to Davenport? (Do not round intermediate calculations. Round your final answer to nearest whole dollar.)

Answer 1

Part 2)

The amount of Davenport's annual retirement payments earned as of the end of 2018 with the use of projected benefits approach is calculated as below:

Annual Retirement Payments = 1.2%*Service Years Till End of 2018*Salary As At End of 2018 = 1.2%*15*230,000 = $41,400

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Part 3)

Step 1: Calculate Present Value of Retirement Annuity As of the Retirement Date (End of 2038)

The present value of retirement annuity as of the retirement date (end of 2038) is determined as below:

Present Value of Retirement Annuity = Annual Retirement Benefits (from Part 2)*PVA(Years,Discount Rate) = 41,400*PVA(18,6%) = 41,400*10.82760 = $448,263 [PVA indicates Present Value of Ordinary Annuity of $1]

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Step 2: Calculate Projected Benefit Obligation At the End of 2018

The value of projected benefit obligation at the end of 2018 is determined as below:

Projected Benefit Obligation at End of 2018 = Present Value of Retirement Annuity (from Step 1)*PV(Year,Rate) = 448,263*PV(20,6%) = 448,263*0.311805 = $139,77 (answer for Part 3) [PV indicates Present Value of $1]

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Part 4)

Step 1: Calculate Annual Retirement Payments as of the End of 2021

The value of annual retirement payment as of the end of 2021 is calculated as follows:

Annual Retirement Payments = 1.2%*Service Years Till End of 2021*Salary As At End of 2021 = 1.2%*18*230,000 = $49,680

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Step 2: Calculate Present Value of Retirement Annuity As of the Retirement Date (End of 2038)

The present value of retirement annuity as of the retirement date (end of 2038) is determined as below:

Present Value of Retirement Annuity = Annual Retirement Benefits (from Part 2)*PVA(Years,Discount Rate) = 49,680*PVA(18,6%) = 49,680*10.82760 = $537,915 [PVA indicates Present Value of Ordinary Annuity of $1]

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Step 3: Calculate Projected Benefit Obligation At the End of 2021

The value of projected benefit obligation at the end of 2021 is determined as below:

Projected Benefit Obligation at End of 2018 = Present Value of Retirement Annuity (from Step 1)*PV(Year,Rate) = 537,915*PV(17,6%) = 537,915*0.37136 = $199,760 (answer for Part 3) [PV indicates Present Value of $1]

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Notes:

There can be a slight difference in final answers on account of rounding off values.